Compact perturbations of 𝑚-accretive operators in Banach spaces

Morales, Claudio

doi:10.1090/S0002-9939-05-08343-7

Compact perturbations of $m$-accretive operators in Banach spaces
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Proc. Amer. Math. Soc. 134 (2006), 365-370 Request permission

Abstract:

This paper continues a discussion that arose twenty years ago, concerning the perturbation of an $m$-accretive operator by a compact mapping in Banach spaces. Indeed, if $A$ is $m$-accretive and $g$ is compact, then the boundary condition $tx \notin A(x)g(x)$ for $x \in \partial G \cap D(A)$ and $t<0$ implies that $0$ is in the closure of the range of $A+g$. Perhaps the most interesting aspect of this result is the proof itself, which does not appeal to the classical degree theory argument used for this type of problem.

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